Should I format USB sticks and SD cards to FAT, FAT32, exFAT or NTFS? (Windows files, live Linux distributions)

Solution 1:

To put it simply:

Between FAT and FAT32, just choose FAT32.
Between NTFS and FAT32, if you use the drive only in Windows, use NTFS. In any other case, use FAT32.

Why NTFS for Windows?

NTFS (New Technology File System) was introduced by Windows and has been supported since the early versions of Windows. So it has become sort of a Windows thing.
Is the native file system for Windows NT, Windows 2000, and Windows XP.
Allows indexing which improves file searching (mostly, faster); causes slight performance hit (can turn off).
Has better security -- such as file-wise encryption (not supported by Windows XP Home edition) and per-user access rules (you can stop your wife from seeing the porn folder!)
Supports user quotas (prevent the tykes from downloading too many MP3 files)
Has file-wise compression.
Is journaled, decreasing data loss (ScanDisk at start up unnecessary).
Uses Unicode (allows foreign and extended character) file names and natively supports long file names.
Supports larger files than FAT (greater than 4 GB).
Allows larger volume sizes (greater than 1 TB). There is talk about a theoretical limit of 16 exabytes, and up to 2 terabytes.
Supported format on dynamic disks (no dynamic disks on Windows XP Home).
Works well with large cache (greater than 96 MB systems).
Performs better on volumes ~20 GB and more.
Is more space-efficient on large volumes (greater than 8 GB).
Resistant to fragmentation.

Why FAT32 for Linux?

FAT32 works well almost everywhere. [FAT32 isn't even the default filesystem on Linux (as opposed to NTFS and Windows)]

Solution 2:

Windows formats USB drives as NTFS by default, FAT is really old, and what type of file system you want to go with depends on your need.

NTFS

Supports files larger than 4 GB
Can run Windows 8 live
UNetbootin does not support NTFS and refuses to use drives that are NTFS formatted.

FAT32

Files must be smaller than 4 GB
Linux Live works

Please know that you can have several partition in your USB device and thereby you can have an NTFS and a FAT32 partition.

Solution 3:

I recommend using UDF, which has roughly the same advantages as NTFS mentioned in @Hele's answer. The biggest reason to use UDF instead of NTFS is OS X compatibility. OS X can only read but not write to NTFS partitions. UDF is well-supported, read-write, on Windows¹, OS X, and Linux.

To format a drive as UDF, see:

Using UDF on a USB flash drive
How to format a flash drive as UDF in Windows 7?

¹ Except Windows XP, which has read-only UDF support